Hom-algebras and Hom-coalgebras were introduced by Makhlouf and Silvestrov in
[1]} as generalizations of ordinary algebras and coalgebras in the following sense: the
associativity of the multiplication is replaced by the Hom-associativity and similar for
Hom-coassociativity. They also defined the structures of Hom-bialgebras and Hom-Hopf
algebras, and described some of their properties extending properties of ordinary bialgebras
and Hopf algebras in [2]} and [3]}.
Recently, many more properties and structures of Hom-Hopf algebras have been developed,
see [4]},[5]}, [6]}, [7]}, [8]},[9]},[10]} and references cited therein.
